Question

The sum of the ages of two brothers is 46. The younger brother is 10 more than a third of the older brothers age. How old is the younger brother?

Answer 1

Set up a system of equations.

x+y=46 where x=older and y=younger
y=10+1/3(x)

Change the form of the first equation to make it easy to combine.

y=46-x
y=10+1/3(x)

Now combine and solve.

46-x=10+1/3(x)
4/3(x)=36
x=27

The older brother is 27, so the younger brother has to be 19.